title: Bijective mapping between the eigenvalue spectrum of a Karle-Hauptman matrix and its phases.
abstract: For any particular Karle-Hauptman matrix, a bijective mapping exists between the eigenvalue spectrum of the matrix and the set of structure-factor phases, given enough phase constraints. For a matrix of order n + 1 with no symmetry-equivalent reflections, n + 1 phases need to be fixed. Only a small subset of matrices derived from centric reflections from trigonal or hexagonal space groups have a bijective mapping without any fixed phases.
authors.affiliation: Department of Mathematics, NUI Maynooth, Maynooth, Co. Kildare, Ireland. adam.ralph@maths.nuim.ie
authors.forename: A C
authors.initials: AC
authors.lastname: Ralph